The photoionization yield is analyzed for three-dimensional quantum systems with finite number of discrete spectrum states driven by unipolar subcycle and few-cycle electromagnetic pulse with a duration much less than "the Kepler period,"electron oscillation period in the ground state. The yield for such objects - symmetric quantum dots and those described by the zero-radius potential - is compared with the yield for hydrogen atom. In all these cases, the standard Keldysh ionization theory is inapplicable. It is shown that ionization probability is determined by the ratio of the electric pulse area (integral of the electric field strength over time) and its characteristic value inversely proportional to the size of the electron localization, and not by the pulse energy or its maximum intensity.